Beam Analysis Workbench

Fig. 1

The model in 3-D

Loading the 3-D view…

Click a support, load, hinge or the foundation to edit it; click the beam to probe the stresses there or to add a load, support or hinge at that point. Drag to orbit, right-drag or Shift-drag to pan, scroll or pinch to zoom. Colours are the exact stresses at the section outline; displacements and twist are exaggerated, and slender sections are drawn enlarged. Ctrl+Z undoes.

Summary

Key results

Fig. 2

Free-body diagrams in two planes

Click anything to edit it, or click the beam to add something there; drag supports, loads, hinges and the ends of distributed loads to move them (snaps to supports and 0.5 % steps; hold Alt for free placement). Reactions are teal, drawn in their actual sense and labelled with magnitudes (signed components are in the summary and the solution); the dashed curve is the exaggerated deflection in each plane. Double-headed arrows are moment vectors along the axis (torques), by the right-hand rule.

Fig. 3

Internal forces and displacements

Choose what to plot. Hover to read values; click or drag to move the probe section. Shift-drag (or Ctrl-scroll) to zoom into a stretch of the beam, double-click to zoom out. Curve colours mark forces, moments, displacements and rotations; blue areas are positive, red negative; jumps are exact one-sided limits at loads and supports. With warping, the torque splits into Saint-Venant and warping parts.

Fig. 4

Cross-section at the probe

Seen from the left end, looking along +x (z to the right, y up). Click the beam in Fig. 1 or drag on this section to move the probe point. C is the centroid, S the shear centre, p₁ and p₂ the principal axes; the dash-dot line is the neutral axis of σ_x. Arrows show the shear flow q = τt along the wall of open sections.

Fig. 5

State of stress at the probe point

A beam fibre carries σ_x and a shear τ along the direction n in the section, so the element is drawn in the x–n plane. Mohr's circle uses Shigley's convention (clockwise shear up); the three circles are the full 3-D state with σ₂ = 0.

Fig. 6

Elastic stability

Fig. 7

Free vibration and critical speed

Fig. 8

Plastic collapse

Fig. 9

Fatigue (stress-life)

Worked solution

Step-by-step derivation with your numbers

Verification

Is the answer right?

Validation suite (runs after the page settles)

Assumptions

What the model assumes, and what changes if it does not hold

Nomenclature

List of symbols and abbreviations

Every symbol used in the figures, results and worked solution, with its meaning and its unit in the current unit system.